Typically this phrase is used when someone invents data or facts to support their argument. Said another way, to "pull something out of your ass".
"This data is a total ass pull!"
This can also be used to describe when, in a TV show or movie, a character comes up with a never-before-seen power just in the nick of time, therefore winning the fight. An ass pull either has a completely unbelievable explanation or the writer conveniently forgets to add one in.
This is most commonly seen in anime (esp. bleach and sailor moon) where the characters are all about to die, but then one of them (in those two, it's almost always Ichigo or Usagi) goes 'oh wait, I forgot about my superawesomeultramove that can kill all the bad guys'.
When Ichigo learns bankai in three days because...um...well...you see this is why it's an ass pull.
Sailor moon aquires 6 different forms throughout the series (7 if you include her normal form), each being inexplicably more powerful than the last. Why? Because she needed to kill the bad guys who were also getting inexplicably more powerful. What, you didn't expect her to lose, did you?
Superman coming up with his 'super-weaving' ability when he needed to make a wedding dress for some reason. Why? Because all superheroes have super-weaving, they just never use it...